Monday, January 16 |
07:00 - 08:45 |
Breakfast ↓ Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |
08:45 - 09:00 |
Introduction and Welcome by BIRS Staff ↓ A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions. (TCPL 201) |
09:00 - 10:00 |
Bao Le Hung: Modelling some non-generic potentially crystalline Emerton-Gee stacks ↓ Potentially crystalline Emerton-Gee stacks are finite type p-adic formal stacks interpolating Kisin's potentially crystalline Galois deformation rings, and are expected to play a critical role in the emerging categorical p-adic Langlands program.
However, even in the simplest non-trivial case of rank 2 tame potentially Barsotti-Tate stacks, these stacks exhibit extremely complicated behaviors when the tame type is non-generic, making them hard to understand.
I will describe a general approach to construct algebraic models for these stacks for tame inertial type and p-small Hodge-Tate weights when p is large. Time permitting, I will talk about several applications, such as the geometric Breuil-Mezard conjecture for generic tame types with close to optimal genericity (joint work in progress with T. Feng), and a conceptualization of computations of Caruso-David-Mezard in the rank 2 tame potentially Barsotti-Tate case (joint work with A. Mezard and S. Morra). (TCPL 201) |
10:00 - 10:30 |
Coffee Break (TCPL Foyer) |
10:30 - 11:30 |
Matthew Emerton: A categorical perspective on the arithmetic Langlands program ↓ A categorical perspective, which has long been the norm in the geometric Langlands program, has recently emerged in the arithmetic Langlands program as well. I will discuss some of the ideas related to this perspective, including the Fargues--Scholze conjecture; conjectures and results (due variously to Ben-Zvi--Chen--Helm--Nadler, Hellmann, Zhu, as well as the speaker, Andrea Dotto, and Toby Gee) regarding fully faithful functors from categories of representations of p-adic reductive groups to categories of coherent sheaves on stacks of Langlands parameters; and conjectural descriptions of the cohomology of locally symmetric congruence quotients (e.g. Shimura varieties) in terms of these categorical ideas. I will try to emphasize the example of modular curves, and the connection to more classical perspectives on modularity, Fontaine--Mazur, and related topics. (TCPL 201) |
11:30 - 13:00 |
Lunch ↓ Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |
13:00 - 14:00 |
Guided Tour of The Banff Centre ↓ Meet in the PDC front desk for a guided tour of The Banff Centre campus. (PDC Front Desk) |
14:00 - 14:20 |
Group Photo ↓ Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo! (TCPL Foyer) |
14:20 - 15:00 |
Free discussion (TCPL 201) |
15:00 - 15:30 |
Coffee Break (TCPL Foyer) |
15:30 - 16:30 |
Florian Herzig: Multivariable (φ,Γ)-modules and local-global compatibility ↓ Suppose that F is a totally real field and v a place dividing p. A (nice) 2-dimensional mod p representation ρ:Gal(¯F/F)→GL2(¯Fp) cuts out a mod p smooth representation π of GL2(Fv) in the cohomology of a Shimura curve. In previous work we constructed a multivariable (φ,Γ)-module DA(π), where Γ=O×K. We show that DA(π)≅D⊗A(ρ|GFv), where GFv is a decomposition group at v and D⊗A is a new functor constructed using perfectoid techniques. This is joint work with C. Breuil, Y. Hu, S. Morra, and B. Schraen. (TCPL 201) |
16:30 - 17:30 |
Catherine Hsu: Explicit non-Gorenstein R=T via rank bounds ↓ In his seminal work on modular curves and the Eisenstein ideal, Mazur studied the existence of congruences between certain Eisenstein series and newforms, proving that Eisenstein ideals associated to weight 2 cusp forms of prime level are locally principal. In this talk, we'll explore generalizations of Mazur's result to squarefree level, focusing on recent work, joint with P. Wake and C. Wang-Erickson, about a non-optimal level N that is the product of two distinct primes and where the Galois deformation ring is not expected to be Gorenstein. First, we will outline a Galois-theoretic criterion for the deformation ring to be as small as possible, and when this criterion is satisfied, deduce an R=T theorem. Then we'll discuss some of the techniques required to computationally verify the criterion. (Online) |
17:30 - 19:30 |
Dinner ↓ A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building. (Vistas Dining Room) |